Herschel did not attain to the knowledge of the ultimate structure of the Universe to which he aspired; but in the course of his long career as an observer and thinker he was led to several discoveries of the greatest importance. The discovery of nebulæ was, of course, one of the objects of his long-continued series of "sweeps" of the heavens. He communicated his first catalogue of 1000 new nebulæ and clusters of stars to the Royal Society in 1788; this was followed three years later by a second catalogue of 1000 similar objects, while in 1802 he drew up a catalogue of 500 "new nebulæ, nebulous stars, planetary nebulae and clusters of stars". He was equally devoted to the study of double stars. These objects, as already mentioned, first attracted his attention because of their suitability for determination of relative stellar parallaxes. But Herschel soon realised that the measurement of the annual parallax of stars was beyond the power of his instruments. His quest for parallaxes from the study of double stars led him to another discovery altogether.
On 10th January, 1782, he communicated to the Royal Society a catalogue of 269 double stars, of which 227 had been discovered by himself; this was succeeded by a second list of 434 in December, 1784. From the beginning of his study of these stellar pairs, he seems to have had a suspicion as to their nature. In the postscript to his first catalogue he said: "In my opinion, it is much too soon to form any theories of small stars revolving round large ones". It was, of course, obvious that double stars might be optical only—caused by two stars happening to lie in the same line of vision. Nevertheless, despite his caution, he kept a careful watch on the relative positions of the components of double star systems for twenty years. In the paper accompanying his catalogue of 500 new nebulæ, read 1st July, 1802, Herschel expressed the view that "casual situations will not account for the multiplied phenomena of double stars," and announced that he was about to communicate a series of observations, from which it would be evident that "many of them have actually changed their situation with regard to each other, in a progressive course, denoting a periodical revolution round each other; and that the motion of some of them is direct, while that of others is retrograde". These observations were tabulated in two papers on "the changes that have happened in the relative situation of double stars," read in 1803 and 1804 respectively. In the first paper, Herschel brought forward evidence in regard to the orbital motions of Alpha Geminorum (Castor), Gamma Leonis, Epsilon Bootis, Zeta Herculis, Delta Serpentis, and Gamma Virginis. The second paper gave details concerning other fifty stars. Herschel also assigned periods to several of the more prominent binaries. These investigations, Herschel claimed, went to prove that many double stars are "not merely double in appearance, but must be allowed to be real binary combinations of two stars intimately held together by the bond of mutual attraction".
The importance of the discovery of binary stars may be realised when we recollect that previously there was no scientific proof of the prevalence of the law of gravitation outside of the Solar System. There were, of course, strong reasons for believing the law to be universal; and John Michell, a man of remarkable sagacity, had argued before Herschel began his observations, that many double stars were certainly binaries. But there was no direct proof until Herschel, after twenty years of patient study, announced his results in 1802. The discovery gave scientific proof of the unity of the Cosmos and of the universal validity of the Newtonian law.
Another brilliant discovery, made almost casually, was announced in 1783 in a paper entitled "On the proper motion of the Sun and Solar System; with an account of several changes that have happened among the fixed stars since the time of Mr. Flamsteed". Halley had in 1718 announced that a number of the brighter stars, so far from being "fixed," in reality were moving through space with considerable velocity. Herschel gave it as his view that "there is not, in strictness of speaking, one fixed star in the heavens". "Now, if the proper motion of the stars in general be once admitted, who can refuse to allow that our Sun, with all its planets and comets, that is, the Solar System, is no less liable to such a general agitation as we find to obtain among all the rest of the celestial bodies?" The idea had occurred to several contemporary astronomers, Wilson, Lalande, and Mayer, but no one had succeeded in attacking the problem practically. It was plainly obvious that the motion of the Sun could only be detected through the resulting apparent motion of the stars, just as the orbital motion of the Earth is reflected in the planetary motions. If the Sun is moving in a certain direction, the stars in front will appear to disperse, while those behind will seem to draw closer together. But the problem is complicated by the individual motions of the "stars; and these motions—themselves very minute—have to be decomposed into two parts, the real motions of the stars themselves and the apparent motion resulting from the translation of the Solar System. "We ought, therefore," said Herschel, "to resolve that which is common to all the stars, which are bound to have what is called a proper motion. into a single real motion of the Solar System, as far as that will answer the known facts, and only to attribute to the proper motion of each particular star the deviations from the general law the stars seem to follow in those movements."
Herschel treated the problem in the simplest manner. Dealing with the proper motions of seven bright stars—Sirius, Castor, Procyon, Pollux, Regulus, Arcturus, and Altair—he separated their real from their apparent motions by simple geometrical methods, and reached the conclusion that the Solar System was moving towards a point in the constellation Hercules, the "apex" of the solar motion being marked by the star Lambda Herculis. "We may," he said, "in a general way estimate that the solar motion can certainly not be less than that which the Earth has in her annual orbit." In 1805, Herschel again attacked the problem, making use of Maskelyne's table of the proper motions of thirty-six stars. His result was in the main confirmatory of his earlier conclusions, the "apex" being again located in the constellation Hercules.
Herschel's brilliant discovery was regarded with considerable incredulity by several of his contemporaries and successors. They seemed to feel that the data on which he worked were too slender for a trustworthy result to be deduced. Bessel, the greatest practical astronomer of the next generation, maintained that there was no evidence in favour of a motion towards a point in Hercules; and even Sir John Herschel rejected his father's conclusions. In 1837, Argelander attacked the question from a study of the motion of 390 stars. The result of his investigation was to confirm abundantly Herschel's conclusions. Since Argelander's time, determination after determination has been made, by many illustrious mathematicians of each generation. Every refinement has been exhausted, "only," in the striking words of Ball, "to confirm the truth of that splendid theory which seems to have been one of the flashes of Herschel's genius".
The light of the stars, no less than their motions, was a favourite subject of study with Herschel. His first communication to the Royal Society dealt with the famous variable star Mira Ceti; and several other papers dealt with the brilliancy of the stars. The problem of stellar variation fascinated him. "Dark spots, or large portions of the surface less luminous than the rest, turned alternately in certain directions, either towards or from us," he wrote in 1796, "will account for all the phenomena of periodical changes in the lustre of the stars so satisfactorily that we certainly need not look for any other cause." But he was aware of other variations—the gradual increase or decrease of the light of certain stars in the course of years or centuries. He regarded as a problem of great practical interest the stability or otherwise of the brilliance of the Sun. His interest in the question of stellar brightness and variation led to his determination of the relative brightness of the stars. Four catalogues of comparative brightness of stars were communicated to the Royal Society the first on 25th February, 1796, the fourth on 21st February, 1799. The observations on which these catalogues were based were made in the years 1795-97, and Herschel seems to have attached so much importance to the work that for three years he discontinued his "sweeping" of the heavens. Two other catalogues were left unpublished at the time of his death, and were first issued in the collected edition of his works. The observations he himself described as "difficult and laborious". He mentioned in the paper accompanying his first catalogue the various causes of error which had to be guarded against, such as moonlight, the different altitudes at which a star might be viewed, the uncertainty of flying cloud, the scintillation of the stars, the zodiacal light, the aurora borealis, and "dew or damp upon the glasses or specula when a telescope is used". Nevertheless, Herschel completed his catalogues, and left behind him a work of imperishable value. For a hundred years the work was under-estimated by astronomers, until, at the close of the nineteenth century, the catalogues were reduced and discussed by the late Professor E. C. Pickering, of Harvard, who gave the following estimate of the value of Herschel's work: "Herschel furnished observations of nearly 3000 stars, from which their magnitudes a hundred years ago can now be determined with an accuracy approaching that of the best modern catalogues. The average difference from the photometric catalogues is only ±0·16, which includes the actual variations of the stars during a century, as well as the errors of both catalogues. The error of a single comparison but little exceeds a tenth of a magnitude."
Herschel's observations of starlight were not only visual and telescopic. In 1798 he passed the light of a few stars of the first magnitude through a prism applied to the eye-glasses of his reflectors. He found that the light of Sirius consisted of red, orange, yellow, green, blue, purple, and violet: that Betelgeux contained the same colours, but that the red was more intense than in Sirius; that Procyon contained more blue and purple, and Arcturus more red and orange than Sirius; that Aldebaran contained much orange; and Vega much yellow, green, blue and purple. Of course, Herschel was unable to discern the dark lines in these spectra, but his observation deserves to be remembered as the first application of the prism to starlight.
It is difficult to know whether to admire most the observational skill or the intellectual grasp displayed in these subsidiary researches; and we cannot but feel, with Arago, "a deep reverence for that powerful genius that has scarcely ever erred".
- Chapter II., p. 19.